# Libraries to help with reading and manipulating data
import pandas as pd
import numpy as np

# libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns

# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)

# to scale the data using z-score
from sklearn.preprocessing import StandardScaler

# to compute distances
from scipy.spatial.distance import cdist, pdist

# to perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# to visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer

# to perform hierarchical clustering, compute cophenetic correlation, and create dendrograms
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage, cophenet

# to suppress warnings
import warnings

warnings.filterwarnings("ignore")

# uncomment and run the following line if using Google Colab
# from google.colab import drive
# drive.mount('/content/drive')

# loading data into a pandas dataframe
data = pd.read_csv("content/marketing_campaign.csv", sep="\t")
data.head()

# Print the datatypes of all the columms
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2240 entries, 0 to 2239
Data columns (total 29 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   ID                   2240 non-null   int64  
 1   Year_Birth           2240 non-null   int64  
 2   Education            2240 non-null   object 
 3   Marital_Status       2240 non-null   object 
 4   Income               2216 non-null   float64
 5   Kidhome              2240 non-null   int64  
 6   Teenhome             2240 non-null   int64  
 7   Dt_Customer          2240 non-null   object 
 8   Recency              2240 non-null   int64  
 9   MntWines             2240 non-null   int64  
 10  MntFruits            2240 non-null   int64  
 11  MntMeatProducts      2240 non-null   int64  
 12  MntFishProducts      2240 non-null   int64  
 13  MntSweetProducts     2240 non-null   int64  
 14  MntGoldProds         2240 non-null   int64  
 15  NumDealsPurchases    2240 non-null   int64  
 16  NumWebPurchases      2240 non-null   int64  
 17  NumCatalogPurchases  2240 non-null   int64  
 18  NumStorePurchases    2240 non-null   int64  
 19  NumWebVisitsMonth    2240 non-null   int64  
 20  AcceptedCmp3         2240 non-null   int64  
 21  AcceptedCmp4         2240 non-null   int64  
 22  AcceptedCmp5         2240 non-null   int64  
 23  AcceptedCmp1         2240 non-null   int64  
 24  AcceptedCmp2         2240 non-null   int64  
 25  Complain             2240 non-null   int64  
 26  Z_CostContact        2240 non-null   int64  
 27  Z_Revenue            2240 non-null   int64  
 28  Response             2240 non-null   int64  
dtypes: float64(1), int64(25), object(3)
memory usage: 507.6+ KB

# Statistical summary of the data
data.describe()

# Average household income
print("Average household income: ", data["Income"].mean())

Average household income:  52247.25135379061

# Find any missing values in the data
missing_data = data.isnull().sum()
print(data.isnull().sum())

# Determine the percentage of missing values in each column
missing_percentage = (missing_data / len(data)) * 100
print(missing_percentage)

ID                      0
Year_Birth              0
Education               0
Marital_Status          0
Income                 24
Kidhome                 0
Teenhome                0
Dt_Customer             0
Recency                 0
MntWines                0
MntFruits               0
MntMeatProducts         0
MntFishProducts         0
MntSweetProducts        0
MntGoldProds            0
NumDealsPurchases       0
NumWebPurchases         0
NumCatalogPurchases     0
NumStorePurchases       0
NumWebVisitsMonth       0
AcceptedCmp3            0
AcceptedCmp4            0
AcceptedCmp5            0
AcceptedCmp1            0
AcceptedCmp2            0
Complain                0
Z_CostContact           0
Z_Revenue               0
Response                0
dtype: int64
ID                     0.000000
Year_Birth             0.000000
Education              0.000000
Marital_Status         0.000000
Income                 1.071429
Kidhome                0.000000
Teenhome               0.000000
Dt_Customer            0.000000
Recency                0.000000
MntWines               0.000000
MntFruits              0.000000
MntMeatProducts        0.000000
MntFishProducts        0.000000
MntSweetProducts       0.000000
MntGoldProds           0.000000
NumDealsPurchases      0.000000
NumWebPurchases        0.000000
NumCatalogPurchases    0.000000
NumStorePurchases      0.000000
NumWebVisitsMonth      0.000000
AcceptedCmp3           0.000000
AcceptedCmp4           0.000000
AcceptedCmp5           0.000000
AcceptedCmp1           0.000000
AcceptedCmp2           0.000000
Complain               0.000000
Z_CostContact          0.000000
Z_Revenue              0.000000
Response               0.000000
dtype: float64

# Since there is less than 5% missing data in the income column we can drop the rows with missing values
data = data.dropna(subset=["Income"])

# Check if the missing values have been removed
print(data.isnull().sum())

ID                     0
Year_Birth             0
Education              0
Marital_Status         0
Income                 0
Kidhome                0
Teenhome               0
Dt_Customer            0
Recency                0
MntWines               0
MntFruits              0
MntMeatProducts        0
MntFishProducts        0
MntSweetProducts       0
MntGoldProds           0
NumDealsPurchases      0
NumWebPurchases        0
NumCatalogPurchases    0
NumStorePurchases      0
NumWebVisitsMonth      0
AcceptedCmp3           0
AcceptedCmp4           0
AcceptedCmp5           0
AcceptedCmp1           0
AcceptedCmp2           0
Complain               0
Z_CostContact          0
Z_Revenue              0
Response               0
dtype: int64

# Check if there are any duplicates in the data
no_of_duplicates = data.duplicated().sum()

if no_of_duplicates == 0:
    print("There are no duplicates in the data")
else:
    print("Row duplicates: ", no_of_duplicates)

There are no duplicates in the data

# Create histograms for numerical columns only
numerical_columns = data.select_dtypes(include=['int64', 'float64']).columns
n_cols = len(numerical_columns) # Number of numerical columns in the dataset
n_rows = (n_cols + 2) // 3  # Ceiling division to determine number of rows needed in the plot

# Create subplots with better spacing and size
fig, axes = plt.subplots(n_rows, 3, figsize=(18, 40))

# Flatten axes array for easier iteration and indexing
axes = axes.flatten()

# Plot histograms with enhanced styling
for idx, col in enumerate(numerical_columns):
    sns.histplot(data=data[col], kde=True, ax=axes[idx])
    axes[idx].set_title(f'Distribution of {col}', fontsize=14)
    axes[idx].set_xlabel(col, fontsize=12)
    axes[idx].set_ylabel('Count', fontsize=12)
    axes[idx].tick_params(labelsize=12)

# Remove any empty plots
for i in range(n_cols, len(axes)):
    fig.delaxes(axes[i])

plt.tight_layout() # Adjust the plots to avoid overlapping
plt.show()

# Create boxplots for numerical columns only
fig, axes = plt.subplots(n_rows, 3, figsize=(10, 40))

# Flatten axes array for easier iteration and indexing
axes = axes.flatten()

# Plot boxplots with enhanced styling
for idx, col in enumerate(numerical_columns):
    sns.boxplot(data=data[col], ax=axes[idx])
    axes[idx].set_title(f'Boxplot of {col}', fontsize=14)
    axes[idx].set_xlabel(col, fontsize=12)
    axes[idx].set_ylabel('Count', fontsize=12)
    axes[idx].tick_params(labelsize=12)

# Remove any empty plots
for i in range(n_cols, len(axes)):
    fig.delaxes(axes[i])

plt.tight_layout() # Adjust the plots to avoid overlapping
plt.show()

# First remove the numerical columns that are not going to add value to the analysis
numerical_columns = numerical_columns.drop(["ID", "AcceptedCmp1", "AcceptedCmp2", "AcceptedCmp3", "AcceptedCmp4", "AcceptedCmp5", "Z_Revenue", "Z_CostContact"])

# Create heatmaps for numerical columns only
corr = data[numerical_columns].corr()

plt.figure(figsize=(12, 8))
sns.heatmap(corr, annot=True, cmap='coolwarm', fmt=".2f")
plt.title("Correlation Heatmap", fontsize=16)
plt.show()

# Create pairplots for numerical columns only
sns.pairplot(data[numerical_columns], diag_kind='kde')
plt.show()

# Scale data from numerical columns
scaler = StandardScaler() # Create a StandardScaler object
data_scaled = scaler.fit_transform(data[numerical_columns]) # Fit and transform the data
pd_data_scaled = pd.DataFrame(data_scaled, columns=numerical_columns) # Convert the scaled data to a dataframe

# Check the first few rows of the scaled data
pd_data_scaled.head()

# Determine the optimal number of clusters using the elbow method
cluster_range = range(2, 15) # Range of clusters to try
inertia_values = [] # List to store the sum of squared distances

# Loop through the range of clusters
for k in cluster_range:
    kmeans_model = KMeans(n_clusters=k, random_state=1) # Create a KMeans model
    kmeans_model.fit(pd_data_scaled) # Fit the model to the scaled data
    inertia_values.append(kmeans_model.inertia_) # Append the sum of squared distances to the list

# Plot the elbow curve
plt.figure(figsize=(12, 8))
plt.plot(cluster_range, inertia_values, marker='o', linestyle='--')
plt.title('Elbow Curve', fontsize=16)
plt.xlabel('Number of Clusters', fontsize=12)
plt.ylabel('Sum of Squared Distances', fontsize=12)
plt.xticks(cluster_range)
plt.grid(True)
plt.show()

# Determine the optimal number of clusters using the silhouette score
silhouette_scores = [] # List to store the silhouette scores
updated_cluster_range = range(2, 10) # Updated range of clusters to try

# Loop through the updated range of clusters
for k in updated_cluster_range:
    kmeans_model = KMeans(n_clusters=k, random_state=1) # Create a KMeans model
    kmeans_model.fit(pd_data_scaled) # Fit the model to the scaled data
    cluster_labels = kmeans_model.predict(pd_data_scaled) # Predict the clusters
    silhouette = silhouette_score(pd_data_scaled, cluster_labels) # Compute the silhouette score
    silhouette_scores.append(silhouette) # Append the silhouette score to the list

# Plot the silhouette scores
plt.figure(figsize=(12, 8))
plt.plot(updated_cluster_range, silhouette_scores, marker='o', linestyle='--')
plt.title('Silhouette Scores', fontsize=16)
plt.xlabel('Number of Clusters', fontsize=12)
plt.ylabel('Silhouette Score', fontsize=12)
plt.xticks(updated_cluster_range)
plt.grid(True)
plt.show()

# Get the time taken to run each model
import time

# List to store the time taken to run each model
time_taken = []

# Loop through the range of clusters and compute the time taken to run each model
for k in updated_cluster_range:
    start = time.time() # Start time
    kmeans_model = KMeans(n_clusters=k, random_state=1) # Create a KMeans model
    kmeans_model.fit(pd_data_scaled) # Fit the model to the scaled data
    end = time.time() # End time
    time_taken.append(end - start) # Append the time taken to the list

# Plot the time taken to run each model
plt.figure(figsize=(12, 8))
plt.plot(updated_cluster_range, time_taken, marker='o', linestyle='--')
plt.title('Time Taken to Run Each Model', fontsize=16)
plt.xlabel('Number of Clusters', fontsize=12)
plt.ylabel('Time Taken (seconds)', fontsize=12)
plt.xticks(updated_cluster_range)
plt.grid(True)
plt.show()

# Create a KMeans model with 4 clusters
kmeans_model = KMeans(n_clusters=4, random_state=1) # Create a KMeans model
kmeans_model.fit(pd_data_scaled) # Fit the model to the scaled data
cluster_labels = kmeans_model.predict(pd_data_scaled) # Predict the clusters
cluster_labels = pd.DataFrame(cluster_labels, columns=['Cluster']) # Convert the cluster labels to a dataframe

# List of distance metrics to try
distance_metrics = ['euclidean', 'chebyshev', 'mahalanobis', 'cityblock']

# List of linkage methods to try
linkage_methods = ['weighted', 'complete', 'average', 'single']

# Initialize the highest cophenetic correlation
highest_cophenetic_correlation = 0
high_dm_lm = [0, 0] # Initialize the distance metric and linkage method with the highest cophenetic correlation

# Loop through the distance metrics
for dm in distance_metrics:
    # Loop through the linkage methods
    for lm in linkage_methods:
        # Calculate the linkage matrix
        Z = linkage(pd_data_scaled, method=lm, metric=dm)

        # Calculate the cophenetic correlation
        c, coph_dists = cophenet(Z, pdist(pd_data_scaled))

        # Update the highest cophenetic correlation and the distance metric and linkage method with the highest cophenetic correlation
        if c > highest_cophenetic_correlation:
            highest_cophenetic_correlation = c
            high_dm_lm = [dm, lm]

# Print the distance metric and linkage method with the highest cophenetic correlation
print("Distance metric and linkage method with the highest cophenetic correlation: ", high_dm_lm)

Distance metric and linkage method with the highest cophenetic correlation:  ['euclidean', 'average']

# List of linkage methods to try for euclidean distance metric
linkage_methods = ['ward', 'complete', 'average', 'single', 'weighted', 'centroid']

# Lists to save results of the cophenetic correlation
cophenetic_correlations = []

# Create subplots for the dendograms
fig, axes = plt.subplots(2, 3, figsize=(18, 12))

# Flatten axes array for easier iteration and indexing
axes = axes.flatten()

# Loop through the linkage methods
for idx, lm in enumerate(linkage_methods):
    # Calculate the linkage matrix
    Z = linkage(pd_data_scaled, method=lm, metric='euclidean')

    # Calculate the cophenetic correlation
    c, coph_dists = cophenet(Z, pdist(pd_data_scaled))

    # Append the cophenetic correlation to the list
    cophenetic_correlations.append(c)

    # Print the cophenetic correlation
    print(f"Cophenetic correlation for {lm}: {c}")

    # Create a dendrogram
    dendrogram(Z, ax=axes[idx])
    axes[idx].set_title(f'Dendrogram ({lm})', fontsize=14)
    axes[idx].set_xlabel('Index', fontsize=12)
    axes[idx].set_ylabel('Distance', fontsize=12)

plt.tight_layout() # Adjust the plots to avoid overlapping
plt.show()

Cophenetic correlation for ward: 0.5531451066946624
Cophenetic correlation for complete: 0.7476365351356612
Cophenetic correlation for average: 0.8641705207861288
Cophenetic correlation for single: 0.7493036915980718
Cophenetic correlation for weighted: 0.5639699100437017
Cophenetic correlation for centroid: 0.8362612686913146

# Get the silhouette scores for hierarchical clustering
silhouette_scores = [] # List to store the silhouette scores
updated_cluster_range = range(2, 15) # Updated range of clusters to try

# Loop through the updated range of clusters
for k in updated_cluster_range:
    hierarchical_model = AgglomerativeClustering(n_clusters=k) # Create an AgglomerativeClustering model
    cluster_labels = hierarchical_model.fit_predict(pd_data_scaled) # Fit the model to the scaled data and predict the clusters
    silhouette = silhouette_score(pd_data_scaled, cluster_labels) # Compute the silhouette score
    silhouette_scores.append(silhouette) # Append the silhouette score to the list  

# Plot the silhouette scores
plt.figure(figsize=(12, 8))
plt.plot(updated_cluster_range, silhouette_scores, marker='o', linestyle='--')
plt.title('Silhouette Scores', fontsize=16)
plt.xlabel('Number of Clusters', fontsize=12)
plt.ylabel('Silhouette Score', fontsize=12)
plt.xticks(updated_cluster_range)
plt.grid(True)
plt.show()

# Create a Hierarchical Clustering model with the optimal number of clusters, distance metric, and linkage method
# Measure the time taken to run the model
start = time.time() # Start time

Hierarchical_model = AgglomerativeClustering(n_clusters=4, linkage='average', metric='euclidean') # Create an AgglomerativeClustering model
Hierarchical_model.fit(pd_data_scaled) # Fit the model to the scaled data

end = time.time() # End time

# Print the time taken to run the model
print("Time taken to run the Hierarchical Clustering model: ", end - start)

Time taken to run the Hierarchical Clustering model:  0.16041946411132812

# Compare the clusters from KMeans and Hierarchical Clustering
# Create a copy of the original data
data_copy = data.copy()
data_scaled_copy = pd_data_scaled.copy()

# Add the KMeans clusters to the copy of the original data
data_copy['KMeans_Clusters'] = kmeans_model.labels_
data_scaled_copy['KMeans_Clusters'] = kmeans_model.labels_

# Add the Hierarchical Clustering clusters to the copy of the original data
data_copy['Hierarchical_Clusters'] = Hierarchical_model.labels_
data_scaled_copy['Hierarchical_Clusters'] = Hierarchical_model.labels_

# Check the first few rows of the copy of the original data
data_copy.head()
data_scaled_copy.head()

# Iterate through the numerical columns and create boxplots for kmeans clusters and hierarchical clusters
plt.figure(figsize=(18, 40))

# Loop through the numerical columns
for idx, col in enumerate(numerical_columns):
    plt.subplot(7, 3, idx + 1) # Create subplots
    sns.boxplot(x='KMeans_Clusters', y=col, data=data_copy) # Create boxplots
    plt.title(f'Boxplot of {col} by KMeans Clusters', fontsize=14) # Set the title
    plt.xlabel('KMeans Clusters', fontsize=12) # Set the x-axis label
    plt.ylabel(col, fontsize=12) # Set the y-axis label

plt.tight_layout() # Adjust the plots to avoid overlapping
plt.show()

# Create boxplots for hierarchical clusters
plt.figure(figsize=(18, 40))

# Loop through the numerical columns
for idx, col in enumerate(numerical_columns):
    plt.subplot(7, 3, idx + 1) # Create subplots
    sns.boxplot(x='Hierarchical_Clusters', y=col, data=data_copy) # Create boxplots
    plt.title(f'Boxplot of {col} by Hierarchical Clusters', fontsize=14) # Set the title
    plt.xlabel('Hierarchical Clusters', fontsize=12) # Set the x-axis label
    plt.ylabel(col, fontsize=12) # Set the y-axis label

plt.tight_layout() # Adjust the plots to avoid overlapping
plt.show()

# Create barplots of numerical columns for KMeans clusters
plt.figure(figsize=(18, 40))

# Loop through the numerical columns
for idx, col in enumerate(numerical_columns):
    plt.subplot(7, 3, idx + 1) # Create subplots
    sns.barplot(x='KMeans_Clusters', y=col, data=data_copy) # Create barplots
    plt.title(f'Barplot of {col} by KMeans Clusters', fontsize=14) # Set the title
    plt.xlabel('KMeans Clusters', fontsize=12) # Set the x-axis label
    plt.ylabel(col, fontsize=12) # Set the y-axis label

plt.tight_layout() # Adjust the plots to avoid overlapping
plt.show()

	ID	Year_Birth	Income	Kidhome	Teenhome	Recency	MntWines	MntFruits	MntMeatProducts	MntFishProducts	MntSweetProducts	MntGoldProds	NumDealsPurchases	NumWebPurchases	NumCatalogPurchases	NumStorePurchases	NumWebVisitsMonth	AcceptedCmp3	AcceptedCmp4	AcceptedCmp5	AcceptedCmp1	AcceptedCmp2	Complain	Z_CostContact	Z_Revenue	Response
count	2240.000000	2240.000000	2216.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.000000	2240.0	2240.0	2240.000000
mean	5592.159821	1968.805804	52247.251354	0.444196	0.506250	49.109375	303.935714	26.302232	166.950000	37.525446	27.062946	44.021875	2.325000	4.084821	2.662054	5.790179	5.316518	0.072768	0.074554	0.072768	0.064286	0.013393	0.009375	3.0	11.0	0.149107
std	3246.662198	11.984069	25173.076661	0.538398	0.544538	28.962453	336.597393	39.773434	225.715373	54.628979	41.280498	52.167439	1.932238	2.778714	2.923101	3.250958	2.426645	0.259813	0.262728	0.259813	0.245316	0.114976	0.096391	0.0	0.0	0.356274
min	0.000000	1893.000000	1730.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	3.0	11.0	0.000000
25%	2828.250000	1959.000000	35303.000000	0.000000	0.000000	24.000000	23.750000	1.000000	16.000000	3.000000	1.000000	9.000000	1.000000	2.000000	0.000000	3.000000	3.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	3.0	11.0	0.000000
50%	5458.500000	1970.000000	51381.500000	0.000000	0.000000	49.000000	173.500000	8.000000	67.000000	12.000000	8.000000	24.000000	2.000000	4.000000	2.000000	5.000000	6.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	3.0	11.0	0.000000
75%	8427.750000	1977.000000	68522.000000	1.000000	1.000000	74.000000	504.250000	33.000000	232.000000	50.000000	33.000000	56.000000	3.000000	6.000000	4.000000	8.000000	7.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	3.0	11.0	0.000000
max	11191.000000	1996.000000	666666.000000	2.000000	2.000000	99.000000	1493.000000	199.000000	1725.000000	259.000000	263.000000	362.000000	15.000000	27.000000	28.000000	13.000000	20.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	3.0	11.0	1.000000

	ID	Year_Birth	Education	Marital_Status	Income	Kidhome	Teenhome	Dt_Customer	Recency	MntWines	MntFruits	MntMeatProducts	MntFishProducts	MntSweetProducts	MntGoldProds	NumDealsPurchases	NumWebPurchases	NumCatalogPurchases	NumStorePurchases	NumWebVisitsMonth	Z_CostContact	Z_Revenue	Response
0	5524	1957	Graduation	Single	58138.0	0	0	04-09-2012	58	635	88	546	172	88	88	3	8	10	4	7	3	11	1
1	2174	1954	Graduation	Single	46344.0	1	1	08-03-2014	38	11	1	6	2	1	6	2	1	1	2	5	3	11	0
2	4141	1965	Graduation	Together	71613.0	0	0	21-08-2013	26	426	49	127	111	21	42	1	8	2	10	4	3	11	0
3	6182	1984	Graduation	Together	26646.0	1	0	10-02-2014	26	11	4	20	10	3	5	2	2	0	4	6	3	11	0
4	5324	1981	PhD	Married	58293.0	1	0	19-01-2014	94	173	43	118	46	27	15	5	5	3	6	5	3	11	0

Problem Statement¶

Business Context¶

Objective¶

Data Dictionary¶

Let's start coding!¶

Importing necessary libraries¶

Loading the data¶

Data Overview¶

Question 1: What are the data types of all the columns?¶

Observations:¶

Question 2: Check the statistical summary of the data. What is the average household income?¶

Observations:¶

Question 3: Are there any missing values in the data? If yes, treat them using an appropriate method¶

Observations:¶

Question 4: Are there any duplicates in the data?¶

Observations:¶

Exploratory Data Analysis¶

Univariate Analysis¶

Question 5: Explore all the variables and provide observations on their distributions. (histograms and boxplots)¶

Observations:¶

Bivariate Analysis¶

Question 6: Perform multivariate analysis to explore the relationsips between the variables.¶

Observations:¶

K-means Clustering¶

Question 7 : Select the appropriate number of clusters using the elbow Plot. What do you think is the appropriate number of clusters?¶

Observations:¶

Question 8 : finalize appropriate number of clusters by checking the silhoutte score as well. Is the answer different from the elbow plot?¶

Observations:¶

Question 9: Do a final fit with the appropriate number of clusters. How much total time does it take for the model to fit the data?¶

Observations:¶

Hierarchical Clustering¶

Question 10: Calculate the cophnetic correlation for every combination of distance metrics and linkage. Which combination has the highest cophnetic correlation?¶

Observations:¶

Question 11: plot the dendogram for every linkage method with "Euclidean" distance only. What should be the appropriate linkage according to the plot?¶

Observations:¶

Question 12: Check the silhoutte score for the hierchial clustering. What should be the appropriate number of clusters according to this plot?¶

Observations:¶

Question 13: Fit the Hierarchial clustering model with the appropriate parameters finalized above. How much time does it take to fit the model?¶

Observations:¶

Cluster Profiling and Comparison¶

K-Means Clustering vs Hierarchical Clustering Comparison¶

Question 14: Perform and compare Cluster profiling on both algorithms using boxplots. Based on the all the observaions Which one of them provides better clustering?¶

Observations:¶

Question 15: Perform Cluster profiling on the data with the appropriate algorithm determined above using a barplot. What observations can be derived for each cluster from this plot?¶

Observations:¶

Business Recommedations¶

1. Focus on Retaining High-Value Customers (Cluster 3)¶

2. Activate Potential in Moderate-Spending Customers (Cluster 2)¶

3. Reengage Low-Value Customers (Cluster 1)¶

4. Convert Browsers into Buyers (Cluster 0)¶

5. Strengthen Digital and Multi-Channel Strategies¶

6. Develop Campaigns to Boost Responses¶

7. Leverage Product-Specific Insights¶